Global pointwise decay estimates for defocusing radial nonlinear wave equations

We prove global pointwise decay estimates for a class of defocusing semilinear wave equations in $n=3$ dimensions restricted to spherical symmetry. The technique is based on a conformal transformation and a suitable choice of the mapping adjusted to the nonlinearity. As a result we obtain a pointwise bound on the solutions for arbitrarily large Cauchy data, provided the solutions exist globally. The decay rates are identical with those for small data and hence seem to be optimal. A generalization beyond the spherical symmetry is suggested.Comment: 9 pages, 1 figur

Optical lattice quantum simulator for QED in strong external fields: spontaneous pair creation and the Sauter-Schwinger effect

Spontaneous creation of electron-positron pairs out of the vacuum due to a strong electric field is a spectacular manifestation of the relativistic energy-momentum relation for the Dirac fermions. This fundamental prediction of Quantum Electrodynamics (QED) has not yet been confirmed experimentally as the generation of a sufficiently strong electric field extending over a large enough space-time volume still presents a challenge. Surprisingly, distant areas of physics may help us to circumvent this difficulty. In condensed matter and solid state physics (areas commonly considered as low energy physics), one usually deals with quasi-particles instead of real electrons and positrons. Since their mass gap can often be freely tuned, it is much easier to create these light quasi-particles by an analogue of the Sauter-Schwinger effect. This motivates our proposal of a quantum simulator in which excitations of ultra-cold atoms moving in a bichromatic optical lattice represent particles and antiparticles (holes) satisfying a discretized version of the Dirac equation together with fermionic anti-commutation relations. Using the language of second quantization, we are able to construct an analogue of the spontaneous pair creation which can be realized in an (almost) table-top experiment.Comment: 21 pages, 10 figure

Multiple homography estimation with full consistency constraints

A novel approach is presented to estimating a set of interdependent homography matrices linked together by latent variables. The approach allows enforcement of all underlying consistency constraints while accounting for the arbitrariness of the scale of each individual matrix. The input data is assumed to be in the form of a set of homography matrices obtained by estimation from image data with the consistency constraints ignored, appended by a set of error covariances associated with these matrix estimates. A cost function is proposed for upgrading, via optimisation, the input data to a set of homography matrices satisfying the constraints. The function is invariant to a change of any of the individual scales of the input matrices. The proposed approach is applied to the particular problem of estimating a set of homography matrices induced by multiple planes in the 3D scene between two views. Experimental results are given which demonstrate the effectiveness of the approach.Wojciech Chojnacki, Zygmunt L. Szpak, Michael J. Brooks and Anton van den Hengelhttp://dicta2010.conference.nicta.com.au

Enforcing consistency constraints in uncalibrated multiple homography estimation using latent variables

An approach is presented for estimating a set of interdependent homography matrices linked together by latent variables. The approach allows enforcement of all underlying consistency constraints while accounting for the arbitrariness of the scale of each individual matrix. The input data is assumed to be in the form of a set of homography matrices individually estimated from image data with no regard to the consistency constraints, appended by a set of error covariances, each characterising the uncertainty of a corresponding homography matrix. A statistically motivated cost function is introduced for upgrading, via optimisation, the input data to a set of homography matrices satisfying the constraints. The function is invariant to a change of any of the individual scales of the input matrices. The proposed approach is applied to the particular problem of estimating a set of homography matrices induced by multiple planes in the 3D scene between two views. An optimisation algorithm for this problem is developed that operates on natural underlying latent variables, with the use of those variables ensuring that all consistency constraints are satisfied. Experimental results indicate that the algorithm outperforms previous schemes proposed for the same task and is fully comparable in accuracy with the ‘gold standard’ bundle adjustment technique, rendering the whole approach both of practical and theoretical interest. With a view to practical application, it is shown that the proposed algorithm can be incorporated into the familiar random sampling and consensus technique, so that the resulting modified scheme is capable of robust fitting of fully consistent homographies to data with outliers.Wojciech Chojnacki, Zygmunt L. Szpak, Michael J. Brooks, Anton van den Henge

Intermediate behavior of Kerr tails

The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed "splitting". We discuss far-field "splitting" in the full field and near-horizon "splitting" in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the "splitting" behavior, and we determine uniquely decay rates that previous studies found to be ambiguous or immeasurable. The far-field "splitting" is explained by competition between projected modes. The near-horizon "splitting" is due to excitation of lower multipole modes that back excite the multipole mode for which "splitting" is observed. In both cases "splitting" is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. We then propose a formula for the decay rate of tails that takes into account the inter--mode excitation effect that we study.Comment: 16 page

Octupole transitions in the 208Pb region

The 208Pb region is characterised by the existence of collective octupole states. Here we populated such states in 208Pb + 208Pb deep-inelastic reactions. γ-ray angular distribution measurements were used to infer the octupole character of several E3 transitions. The octupole character of the 2318 keV 17− → 14+ in 208Pb, 2485 keV 19/2 − → 13/2 + in 207Pb, 2419 keV 15/2 − → 9/2 + in 209Pb and 2465 keV 17/2 + → 11/2 − in 207Tl transitions was demonstrated for the first time. In addition, shell model calculations were performed using two different sets of two-body matrix elements. Their predictions were compared with emphasis on collective octupole states.This work is supported by the Science and Technology Facilities Council (STFC), UK, US Department of Energy, Office of Nuclear Physics, under Contract No. DEAC02-06CH11357 and DE-FG02-94ER40834, NSF grant PHY-1404442

Charged particle decay of hot and rotating 88^{88}Mo nuclei in fusion-evaporation reactions

A study of fusion-evaporation and (partly) fusion-fission channels for the $^{88}$Mo compound nucleus, produced at different excitation energies in the reaction $^{48}$Ti + $^{40}$Ca at 300, 450 and 600 MeV beam energies, is presented. Fusion-evaporation and fusion-fission cross sections have been extracted and compared with the existing systematics. Experimental data concerning light charged particles have been compared with the prediction of the statistical model in its implementation in the Gemini++ code, well suited even for high spin systems, in order to tune the main model parameters in a mass region not abundantly covered by exclusive experimental data. Multiplicities for light charged particles emitted in fusion evaporation events are also presented. Some discrepancies with respect to the prediction of the statistical model have been found for forward emitted $\alpha$-particles; they may be due both to pre-equilibrium emission and to reaction channels (such as Deep Inelastic Collisions, QuasiFission/QuasiFusion) different from the compound nucleus formation.Comment: 14 pages, 14 figure

Angular distributions of rays from 210bi produced in 208 pb+208pb deep-inelastic reactions

The high-spin yrast structure of the 210Bi nucleus was investigated using -ray coincidence spectroscopy following deep-inelastic reactions in the 208Pb+208Pb system. Cascades of rays following the decay of a new isomer were identified. Spin-parity assignments to the states known from previous studies as well as to newly located excitations were made based on the measured angular distributions of rays combined with a transition conversion coefficient analysis

Reduction in the uncertainty of the neutron-capture cross section of 210Bi: Impact of a precise multipolarity measurement of the 2− → 1− main ground-state transition

International audience; The mixing ratio of the main 320-keV, M1 + E2 ground-state γ transition in 210Bi has been more precisely quantified, allowing a significant reduction in the uncertainty of measurements of the neutron-capture cross section to the ground state of 210Bi from 25% to 0.9%. Accurate values for neutron-capture cross sections to both the ground and long-lived 9− isomeric state at 271 keV in 210Bi are of particular importance as Pb-Bi finds increased usage in Accelerator Driven Systems